Robust watermarking using orthogonal Fourier–Mellin moments and chaotic map for double images
Introduction
With the rapid development of Internet and convenient access to digital devices, digital images are more easily acquired and distributed than ever before, which also raises the issues of illegal usage and malicious manipulation. Thus it is necessary to take actions to deal with these issues. As a useful mechanism for copyright authentication for multimedia, image watermarking has been investigated extensively [1], [2], which is to embed some secret information (e.g., a logo, some text or an identifier) into the original image that can be retrieved for ownership authentication when necessary.
Over the past two decades, significant progresses have been made in image watermarking techniques [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]. In early approaches, a watermark was typically embedded into the host image through modifying its pixel values directly. However, it is not robust enough to use this kind of watermarking schemes. To improve the robustness, it becomes prevailing to implement watermarking in the transform domain. Among various image watermarking techniques, the lossless schemes are preferred to keep the image fidelity. The main approaches can be roughly classified into reversible watermarking and zero-watermarking schemes [15]. For the latter, it usually generates watermarks by means of important features from an image rather than modifying its pixel values or transformation coefficients, and the watermarking is registered in the Trusted Authority through a secure channel, which is responsible for image authentication in future use. It is the merit of zero-watermark copyright authentication that makes it suitable especially for medical images, remote sensing imagery and military applications. For example, a small change in a medical image due to embedding of secret information may affect the interpretation significantly or result in misdiagnosis [3]. Currently, there are many feature descriptors that can be selected for constructing the zero-watermark. For example, Wen et al. [8] employed third-order and fourth-order cumulants to construct a zero-watermark scheme. Jing and Liu [9] presented a novel zero-watermark generation approach by combining discrete wavelet transform, log-polar mapping and scale invariant feature transform. Fan et al. [10] introduced a lifting wavelet and Harris corner detection based zero-watermarking, but the stability of the approach is sensitive with respect to the parameters such as the threshold value and the radius of a local feature region. Wu and Sun [11] utilized overlapping discrete cosine transform (DCT) and singular value decomposition (SVD) to construct ownership information. By combing the visual cryptography technique, Lou et al. [12] addressed a copyright protection scheme based on discrete wavelet transforms. In the scheme addressed by Rawat and Raman [13], an image was firstly divided into small non-overlapping blocks, then the top singular values of fractional Fourier transformed subimages were used to construct a zero-watermark. Liu and Wu [14] proposed a robust zero-watermark scheme making use of multiple techniques including two-level discrete wavelet transform, chaos technique, noise reduction and error correcting code. In addition, due to its remarkable characteristics such as being insensitive to noise, low information redundancy and configurable invariants to geometric transformation (translation, scaling or rotation), orthogonal moment and moment invariants have been used in the community of image watermarking [20], [21], [22], [23]. To satisfy the rotation invariance, a zero-watermarking scheme was established based on the modulus of Bessel–Fourier moments (BFMs) [15]. Zhang et al. [16] derived a set of affine Legendre moment invariants and used them for embedding, detection and restitution of watermarking. Based on the concept of communications with side information, Lu [17] designed a robust block-DCT side-informed watermarking scheme, where a moment normalization was used to solve geometric distortions.
For the zero-watermark copyright authentication schemes discussed above, the main focus is on a single image. These techniques may be used repeatedly for multiple images. However, it will be time consuming and will occupy more storage space in registration. On the other hand, the schemes used in [10], [11], [12], [13], [14], [15] require normalizations when the host images have geometric distortions. To overcome these shortcomings, we develop a novel zero-watermarking scheme that can realize copyright authentication for double images, while improving the efficiency of watermarking systems and saving the storage space simultaneously. Our approach integrates two host images into a single-channel architecture with the help of a complex representation, and utilizes the orthogonal Fourier–Mellin moment to extract image features that are invariant to rotation and scaling. Then we construct a binary feature image, which is crucial to the generation of a verification image. Moreover, a chaotic map is computed to strengthen the confidentiality of the proposed scheme. Experimental results demonstrate that the proposed scheme is more reliable than others and can be applied well to copyright protection.
The rest of this paper is organized as follows. Section 2 presents two main techniques used in the proposed watermarking scheme. The detailed description of our novel watermarking approach is presented in Section 3. The performance of the proposed scheme is validated with a series of experiments in Section 4, and finally some conclusions are drawn in Section 5.
Section snippets
Preliminaries
In this section, two main techniques are briefly described, including the orthogonal Fourier–Mellin moments and a chaotic map. For the orthogonal Fourier–Mellin moments, a kind of scaling and rotation invariants are introduced. A similar proof of the invariance can be found in [23].
Proposed scheme
The proposed image watermarking scheme makes use of a complex representation, based on the orthogonal Fourier–Mellin moments and Hénon map. Similar to the existing congeneric schemes, our scheme has ownership registration and ownership verification phases. In the first phase, the owners complete the registration of verification image secretly. Once the attackers modify or use the watermarked images illegally, the owners can declare their ownership through the extracted watermark.
Experiments
To evaluate the validity and feasibility of the proposed watermarking scheme, a great variety of experiments have been carried out. 60 grayscale images with the size of 256×256 and selected from the CVG-UGR database [28], which are used as the test sets. Five binary images with the size of 64×64 were downloaded from the Internet, which are used as watermarks (shown in Fig. 1). The initializations of Hénon map employed to scramble the feature images and watermarks are (0.15, −0.25) and (0.30,
Conclusion
We have presented a robust watermarking scheme based on the orthogonal Fourier–Mellin moments and Hénon map for double images, which has achieved a high level security and occupied less storage space. Both the ownership registration and ownership verification phases are included in the proposed method. The invariants derived from orthogonal Fourier–Mellin moments were utilized to construct the feature image. Together with the scrambled watermark, the verification image can be generated and
Acknowledgments
This work was supported by the Project of Construction of Innovative Teams and Teacher Career Development for Universities and Colleges under Beijing Municipality. The authors thank the editor and anonymous reviewers for their constructive comments and valuable suggestions that greatly improve the paper.
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